To prepare a high-quality connection between a fitting and an end of a composite pipe, the end of the composite pipe to be connected also must be calibrated if it is noncircular. Calibration is necessary especially because the pipe end is usually deformed during the cutting off of the pipe. A tool of the above-described class has hitherto been used for this purpose. This has, on a holder, a burr for deburring and a plurality of pins with a cylindrical area, corresponding to the usual pipe sizes, for calibration. Using this tool, the pipe end to be connected was deburred on the inside with the burr and calibrated on the calibrating pin corresponding to this pipe end after the composite pipe had been cut by means of a pipe cutter. The pipe thus prepared was subsequently pushed over the fitting and pressed with a jointing clamp. The calibration and deburring are essentially installation steps for preparing tight pressed connections, which have proved to be extremely successful especially in interior installations.